Because it's an anniversary part of me says that it's not just about the food and that the location and ambiance are big factors. I think both menus are great and you will enjoy the food at either place, but being in a small, cozy restaurant in the Village seems to me to be a better vibe than a restaurant in midtown in a hotel.

Haven't been to Ai Fiori, but highly recommend Annisa for all of the reasons mentioned here. Food was some of the best I've had recently and the ambiance is perfectly suited for an anniversary celebration. Now that you mention it, mine is coming up next month so I may make a reservation there. Either way, Happy Anniversary and enjoy!